# Thread: Simple national Income Models

1. ## Simple national Income Models

I'm not overly concerned what the answer to this is however I would appreciate it greatly if someone could at least point me in the correct direction as I am currently cluelessly !!!!

A simple national income model is given by
Y = C + I* + G*
C = a + bY (a > 0 and 0 < b < 1)
for some constants a and b and where I*, G* are exogenous variables.

Find the equilibrium solution for Y and C, and hence deduce the multiplier for G* on C.

2. Subsititute C = a + bY into the first expression.

$Y = a + bY + I + G$

$Y(1-b) = a + I + G$

$Y = \frac{a + I + G}{1-b}$

So an increase of £1 to G will cause an increase of $\frac{1}{1-b}$ in Y. Hence the multiplier is $\frac{1}{1-b}$

Why is this an equilibrium?
if you are interested in understanding this; You can think of the model as trying to find a level of national production (Y) at which there is exactly enough demand (C + I + G) to consume the production.

3. Originally Posted by SpringFan25
Subsititute C = a + bY into the first expression.

$Y = a + bY + I + G$

$Y(1-b) = a + I + G$

$Y = \frac{a + I + G}{1-b}$

So an increase of £1 to G will cause an increase of $\frac{1}{1-b}$ in Y. Hence the multiplier is $\frac{1}{1-b}$

Why is this an equilibrium?
if you are interested in understanding this; You can think of the model as trying to find a level of national production (Y) at which there is exactly enough demand (C + I + G) to consume the production.
I cant believe it was that easy...I got to that point by substitution and what not but couldnt deduce the multiplier....numpty or what! cheers mate

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### national income model

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